A041922 Numerators of continued fraction convergents to sqrt(483).
21, 22, 945, 967, 41559, 42526, 1827651, 1870177, 80375085, 82245262, 3534676089, 3616921351, 155445372831, 159062294182, 6836061728475, 6995124022657, 300631270680069, 307626394702726, 13220939848194561
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,44,0,-1).
Crossrefs
Cf. A041923.
Programs
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Magma
I:=[21, 22, 945, 967]; [n le 4 select I[n] else 44*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013
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Mathematica
Numerator[Convergents[Sqrt[483], 30]] (* or *) CoefficientList[Series[-(x^3 - 21 x^2 - 22 x - 21)/(x^4 - 44 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *) LinearRecurrence[{0,44,0,-1},{21,22,945,967},20] (* Harvey P. Dale, Sep 28 2023 *)
Formula
G.f.: -(x^3-21*x^2-22*x-21)/(x^4-44*x^2+1). - Vincenzo Librandi, Nov 12 2013
a(n) = 44*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 12 2013